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If P is the incenter of A JKL, find each measure. K 10 M P 7 17 32" 22' L

Sagot :

Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).

Based on the property of incenter, the measurements of the sides and the angles will be:

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m∠K = 36°

By using the property of incenter:

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By using the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

Then, from ΔJMP,

tan(32°) = MP/MJ

tan(32°) =  7/MJ

MJ =  7/tan(32)°

MJ = 11.20

And from ΔPOL,

tan(22°) = OP/OL

tan(22°) = 7/OL

OL = 17.33

And from ΔKNP,

tan(36°) = NP/KN

tan(36°) = 7/KN

KN = 9.63

Hence, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

Learn more about incentre of triangle at: https://brainly.com/question/29634968

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